Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 9x + 3$ and $ JT = 2x + 10$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {9x + 3} = {2x + 10}$ Solve for $x$ $ 7x = 7$ $ x = 1$ Substitute $1$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 9({1}) + 3$ $ JT = 2({1}) + 10$ $ CJ = 9 + 3$ $ JT = 2 + 10$ $ CJ = 12$ $ JT = 12$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {12} + {12}$ $ CT = 24$